Question

Evaluate: \[ \int \frac{3x\sec^2\!\sqrt{9x^2-12x+1} -\sec^2\!\sqrt{(3x-2)^2-3}} {\sqrt{9x^2-12x+1}} \,dx \]

• A. \(\sqrt{9x^2-12x+1}+C\)
• B. \(\dfrac13\cos\sqrt{9x^2-12x+1}+C\)
• C. \(\dfrac1{2\sqrt{9x^2-12x+1}}+C\)
• D. None of these

Hint:

Whenever you see \[ \sec^2(f(x)) \] or \[ \csc^2(f(x)), \] immediately check whether the remaining part of the integrand is proportional to \(f'(x)\). If it is, direct substitution solves the problem in one step.

Answer 1

The Correct Option is B